Exercises of Ordinary Differential Equations E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2023

Beschreibung

In this book, exercises are carried out regarding the following mathematical topics: solving differential equations of various orders systems of differential equations Cauchy and Neumann initial value problems. Initial theoretical hints are also presented to make the conduct of the exercises understandable.

Leseprobe

Simone Malacrida

Exercises of Ordinary Differential Equations

BookRix GmbH & Co. KG81371 Munich

Table of Contents

Table of Contents

“Exercises of Ordinary Differential Equations”

INTRODUCTION

THEORETICAL OUTLINE

EXERCISES

“Exercises of Ordinary Differential Equations”

“Exercises of Ordinary Differential Equations”

SIMONE MALACRIDA

In this book, exercises are carried out regarding the following mathematical topics:

solving differential equations of various orders

systems of differential equations

Cauchy and Neumann initial value problems.

Initial theoretical hints are also presented to make the conduct of the exercises understandable.

Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I – THEORETICAL OUTLINE

Introduction and definitions

Resolution methods

Solutions

Remarkable differential equations

Autonomous systems

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II – EXERCISES

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

Exercise 17

Exercise 18

Exercise 19

Exercise 20

Exercise 21

Exercise 22

Exercise 23

Exercise 24

Exercise 25

Exercise 26

Exercise 27

Exercise 28

Exercise 29

Exercise 30

Exercise 31

Exercise 32

Exercise 33

Exercise 34

Exercise 35

Exercise 36

Exercise 37

INTRODUCTION

INTRODUCTION

In this workbook, some examples of calculations relating to ordinary differential equations are carried out.

Furthermore, the main theorems used in differential analysis of equations are presented.

Ordinary differential equations represent a fundamental point in mathematical analysis as, through their resolution, it is possible to answer many physical and technological problems.

In order to understand in more detail what is presented in the resolution of the exercises, the theoretical reference context is recalled in the first chapter.

What is presented in this workbook is generally addressed in advanced mathematical analysis courses (analysis 2).

I

THEORETICAL OUTLINE

THEORETICAL OUTLINE

Introduction and definitions

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A differential equation is a relationship between a function and some of its derivatives.

An equation defined in an interval of the set of real numbers in which the total derivatives of the function with respect to the unknown are present is called ordinary.

The order of the highest derivative in the equation is called the order of the equation.

One can generalize the defining set of an ordinary differential equation into an open and connected generic contained in the complex space of dimension greater than two.

A solution or integral of the ordinary differential equation is a function that satisfies the equation's relation.

An equation is said to be autonomous if the relation does not explicitly depend on the variable and is said to be written in normal form if it can be made explicit with respect to the derivative of maximum degree.

The equation is called linear if the solution is a linear combination of the derivatives according to this formula:

The term r(x) is called source and, if it is zero, the linear differential equation is called homogeneous .

In general, an ordinary differential equation of degree n has n linearly independent solutions, and any linear combination of them is itself a solution.

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